Polynomial features in Data Analysis Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of polynomial feature transformation

What is the output of this code that creates polynomial features of degree 2 for a simple dataset?

Data Analysis Python

from sklearn.preprocessing import PolynomialFeatures
import numpy as np
X = np.array([[2, 3]])
poly = PolynomialFeatures(degree=2, include_bias=False)
result = poly.fit_transform(X)
print(result)

A [[1. 2. 3. 4. 6. 9.]]

B [[2. 3. 4. 9. 6.]]

C [[2. 3. 4. 6. 9.]]

D [[2. 3. 5. 6. 9.]]

💡 Hint

Remember polynomial features include original features and their combinations up to the given degree.

PolynomialFeatures with degree=2 and include_bias=False outputs original features, their squares, and their pairwise products in order: x1, x2, x1^2, x1*x2, x2^2.

❓ data_output

intermediate

Number of features after polynomial expansion

If you have 3 original features and apply PolynomialFeatures with degree=3 and include_bias=True, how many features will the transformed data have?

A 19

B 20

C 15

D 10

💡 Hint

Use the formula for combinations with repetition: (n + d)! / (d! * n!) where n=features, d=degree.

With 3 features and degree 3, total features = C(3+3,3) = C(6,3) = 20 including bias.

🔧 Debug

advanced

Identify the error in polynomial feature usage

What error will this code raise when trying to transform data with PolynomialFeatures?

Data Analysis Python

from sklearn.preprocessing import PolynomialFeatures
poly = PolynomialFeatures(degree=2)
X = [[1, 2], [3, 4, 5]]
poly.fit_transform(X)

A ValueError: Found array with inconsistent numbers of features (2 vs 3)

B TypeError: 'list' object is not callable

C IndexError: list index out of range

D No error, outputs transformed array

💡 Hint

Check if all rows have the same number of features.

The input list has rows with different lengths, causing ValueError about inconsistent feature numbers.

🚀 Application

advanced

Choosing polynomial degree for regression

You have a dataset with one feature and want to fit a polynomial regression model. Which degree choice is best to avoid overfitting while capturing non-linearity?

A Degree 20

B Degree 1 (linear)

C Degree 10

D Degree 2 or 3

💡 Hint

Higher degrees can fit noise, lower degrees may miss patterns.

Degree 2 or 3 balances capturing curves without too much overfitting common in very high degrees.

🧠 Conceptual

expert

Effect of include_bias parameter in PolynomialFeatures

What is the effect of setting include_bias=False in PolynomialFeatures on the transformed data?

A The output excludes the constant term (all ones column).

B The output excludes all original features.

C The output includes only the constant term.

D The output includes only interaction terms, no powers.

💡 Hint

Bias means the constant feature of ones.

include_bias=False removes the constant column of ones from the output features.